### The sum of n terms of an A.P. is 3$\mathbf{n}^{\mathbf{2}}$ + 5n, then 164 is its.

A. 24th term B. 27th term C. 26th term D. 25th term Answer: Option B

### Solution(By Apex Team)

$\begin{array}{l} \text { Sum of } n \text { terms }\left(S_{n}\right)=3 n^{2}+5 n\\ \therefore \text { Sum of }(n-1) \text { terms }\left(S_{n-1}\right)\\ =3(n-1)^{2}+5(n-1)\\ =3\left(n^{2}-2 n+1\right)+5 n-5\\ =3 n^{2}-6 n+3+5 n-5\\ =3 n^{2}-n-2\\ \therefore n^{t h} \text { term }=S_{n}-S_{n-1}\\ \Rightarrow a_{n}=3 n^{2}+5 n-3 n^{2}+n+2\\ a_{n}=6 n+2, \text { But } a_{n}=164\\ \Rightarrow 6 n+2=164\\ \Rightarrow 6 n=164-2\\ \Rightarrow 6 n=162 \end{array}$ So, n = $\Large\frac{162}{6}$ = 27th term

A. 22
B. 25
C. 23
D. 24

A. 5
B. 6
C. 4
D. 3

A. -45
B. -55
C. -50
D. 0